6. Chemical Quantities & Aqueous Reactions

Solution Stoichiometry

Solution Stoichiometry - Explained

A solution is made by mixing 1.5 g of LiOH and 23.5 mL of
1.000 M HNO3. (b) Calculate the
concentration of Li+ remaining in solution.

Copper reacts with dilute nitric acid according to the following equation: 
If a copper penny weighing 3.045 g is dissolved in a small amount of nitric acid and the resultant solution is diluted to 50.0 mL with water, what is the molarity of the Cu(NO3)2?

A 55.0-mL sample of a 0.102 M potassium sulfate solution is
mixed with 35.0 mL of a 0.114 M lead(II) acetate solution and
this precipitation reaction occurs:
K2SO4(aq) + Pb(C2H3O2)2(aq)¡2 KC2H3O2(aq) + PbSO4(s)
The solid PbSO4 is collected, dried, and found to have a mass of
1.01 g. Determine the limiting reactant, theoretical yield, percent yield.

The commercial production of nitric acid involves the
following chemical reactions:
4 NH31g2 + 5 O21g2¡4 NO1g2 + 6 H2O1g2
2 NO1g2 + O21g2¡2 NO21g2
3 NO21g2 + H2O1l2¡2 HNO31aq2 + NO1g2
(c) How many grams
of ammonia must you start with to make 1000.0 L of a 0.150 M
aqueous solution of nitric acid? Assume all the reactions give
100% yield.

Pennies minted after 1982 are mostly zinc (97.5%) with a copper cover. If a post-1982 penny is dissolved in a small amount of nitric acid, the copper coating reacts as in Problem 4.52, and the exposed zinc reacts according to the following equation: 
For a penny that weighs 2.482 g, what is the molarity of the Zn(NO3)2 if the resultant solution is diluted to 250.0 mL with water?

Molarity, Solution Stoichiometry and Dilution Problem

A flask containing 450 mL of 0.500 M HBr was accidentally knocked to the floor. How many grams of K2CO3 would you need to put on the spill to neutralize the acid according to the following equation?

What is the molarity of ZnCl2 that forms when 25.0 g of zinc
completely reacts with CuCl2 according to the following reaction?
Assume a final volume of 275 mL.
Zn(s) + CuCl2(aq)¡ZnCl2(aq) + Cu(s)

Calcium levels in blood can be determined by adding oxa-late ion to precipitate calcium oxalate, CaC2O4, followed by dissolving the precipitate in aqueous acid and titrating the resulting oxalic acid (H2C2O4) with KMnO4: 
How many milligrams of Ca2+ are present in 10.0 mL of blood if 21.08 mL of 0.000 988 M KMnO4 solution is needed for the titration?

How many milliliters of 2.00 M HCl must be added to neutralize the following solutions? 
(b) A mixture of 0.120 M NaOH (350.0 mL) and 0.190 M HBr (150.0 mL)

Describe how you would prepare each of the following 
aqueous solutions, starting with solid KBr:
(d) a 0.150 M solution of KBr that contains just enough KBr to precipitate 16.0 g of AgBr from a
solution containing 0.480 mol of AgNO3.

How many milliliters of 1.00 M KOH must be added to neutralize the following solutions?
(a) A mixture of 0.240 M LiOH (25.0 mL) and 0.200 M HBr (75.0 mL)

The arsenic in a 1.22-g sample of a pesticide was converted to
AsO43- by suitable chemical treatment. It was then titrated
using Ag+ to form Ag3AsO4 as a precipitate. (c) If it took 25.0 mL of 0.102 M Ag+to reach the equivalence point in this titration, what is the mass percentage of arsenic in the pesticide?

When 75.0 mL of a 0.100 M lead(II) nitrate solution is mixed with 100.0 mL of a 0.190 M potassium iodide solu-tion, a yellow-orange precipitate of lead(II) iodide is formed. What is the mass in grams of lead(II) iodide formed? Assume the reaction goes to completion. (LO 4.11, 4.15)
(a) 1.729 g
(b) 3.458 g
(c) 4.380 g 
(d) 8.760 g

Salicylic acid, used in the manufacture of aspirin, contains only the elements C, H, and O and has only one acidic hydrogen that reacts with NaOH. When 1.00 g of salicylic acid undergoes complete combustion, 2.23 g CO2 and 0.39 g H2O are obtained. When 1.00 g of salicylic acid is titrated with 0.100 M NaOH, 72.4 mL of base is needed for complete reaction. What are the empirical and molecular formulas of salicylic acid?

A 0.5895-g sample of impure magnesium hydroxide is dissolved 
in 100.0 mL of 0.2050 M HCl solution. The excess acid 
then needs 19.85 mL of 0.1020 M NaOH for neutralization. 
Calculate the percentage by mass of magnesium hydroxide 
in the sample, assuming that it is the only substance reacting 
with the HCl solution.

Standardized solutions of KBrO3 are frequently used in redox titrations. The necessary solution can be made by dissolving KBrO3 in water and then titrating it with an As(III) solution. What is the molar concentration of a KBrO3 solution if 28.55 mL of the solution is needed to titrate 1.550 g of As2O3? See Problem 4.128 for the balanced equation. (As2O3 dissolves in aqueous acid solution to yield H3AsO3: As2O3 + 3 H2OS 2 H3AsO3.)

How many milliliters of 2.00 M HCl must be added to neutralize the following solutions? 
(a) A mixture of 0.160 M HNO3 (100.0 mL) and 0.100 M KOH (400.0 mL)

Four solutions are prepared and mixed in the following order: (a) Start with 100.0 mL of 0.100 M BaCl2 (b) Add 50.0 mL of 0.100 M AgNO3 (c) Add 50.0 mL of 0.100 M H2SO4 (d) Add 250.0 mL of 0.100 M NH3.
Write an equation for any reaction that occurs after each step, and calculate the concentrations of Ba2+, Cl-, NO3-, NH3, and NH4+ in the final solution, assuming that all reactions go to completion.

A compound that contains only C and H was burned in excess O2 to give CO2 and H2O. When 0.270 g of the com- pound was burned, the amount of CO2 formed reacted completely with 20.0 mL of 2.00 M NaOH solution according to the equation
2 OH-1aq2 + CO21g2 S CO 2- 1aq2 + H2O1l2
When 0.270 g of the compound was dissolved in 50.0 g of camphor, the resulting solution had a freezing point of 177.9 °C. [#Pure camphor freezes at 179.8 °C and has Kf = 37.7 1°C kg2>mol.] (a) What is the empirical formula of the compound?

Trifluoroacetic acid has the chemical formula CF3CO2H.
It is a colorless liquid that has a density of 1.489 g/mL.
(d) How many milliliters of
a 0.500 M solution of NaOH would it take to neutralize
10.5 mL of trifluoroacetic acid?

Potassium permanganate (KMnO4) reacts with oxalic acid (H2C2O4) in aqueous sulfuric acid according to the follow-ing equation: 
How many milliliters of a 0.250 M KMnO4 solution are needed to react completely with 3.225 g of oxalic acid?

Morphine has the formula C17H19NO3. It is a base and accepts
one proton per molecule. It is isolated from opium. A 0.682-g
sample of opium is found to require 8.92 mL of a 0.0116 M solution
of sulfuric acid for neutralization. Assuming that morphine
is the only acid or base present in opium, calculate the
percent morphine in the sample of opium.

How many milliliters of 0.250 M Na2S2O3 solution is needed for complete reaction with 2.486 g of I2 according to the equation in Problem 4.124?

A 25.0-mL sample of a 1.20 M potassium chloride solution is
mixed with 15.0 mL of a 0.900 M lead(II) nitrate solution and
this precipitation reaction occurs:
2 KCl(aq) + Pb(NO3)2(aq)¡ PbCl2(s) + 2 KNO3(aq)
The solid PbCl2 is collected, dried, and found to have a mass of
2.45 g. Determine the the percent yield.

The odor of skunks is caused by chemical compounds called thiols. These compounds, of which butanethiol (C4H10S) is a representative example, can be deodorized by reaction with household bleach (NaOCl) according to the following equation: according to the following equation?

How many grams of butanethiol can be deodorized by reac-tion with 5.00 mL of 0.0985 M NaOCl?

Compound X contains only the elements C, H, O, and S. A 5.00 g sample undergoes complete combustion to give 4.83 g of CO2, 1.48 g of H2O, and a certain amount of SO2 that is further oxidized to SO3 and dissolved in water to form sulfuric acid, H2SO4. On titration of the H2SO4, 109.8 mL of 1.00 M NaOH is needed for complete reaction. (Both H atoms in sulfuric acid are acidic and react with NaOH.)
(a) What is the empirical formula of X?

A volume of 18.72 mL of 0.1500 M K2Cr2O7 solution was required to titrate a sample of FeSO4 according to the equation in Problem 4.126. What is the mass of the sample?

(b) What is the mass of each substance in the original 250 g mixture?

The “free-base” form of cocaine (C17H21NO4) and its protonated hydrochloride form (C17H22ClNO4) are shown
below; the free-base form can be converted to the hydrochloride form with one equivalent of HCl. For clarity, not
all the carbon and hydrogen atoms are shown; each vertex
represents a carbon atom with the appropriate number of
hydrogen atoms so that each carbon makes four bonds to
other atoms

(e) How many mL of a concentrated 18.0 M HCl aqueous solution would it take to convert 1.00 kilograms 
(a “kilo”) of the free-base form of cocaine into its hydrochloride form?

Solution Stoichiometry tutorial: How to use Molarity + problems explained | Crash Chemistry Academy

(b) What volume of
0.128 M HCl is needed to neutralize 2.87 g of Mg1OH22? 

A sample weighing 14.98 g and containing a small amount of copper was treated to give a solution containing aque-ous Cu2+ ions. Sodium iodide was then added to yield solid copper(I) iodide plus I3 with thiosulfate, S2O3 - ion, and the I3 - was titrated 2-. The titration required 10.49 mL of 0.100 M Na2S2O3 for complete reaction. What is the mass percent copper in the sample? The balanced equations are

Iron content in ores can be determined by a redox procedure in which the sample is first reduced with Sn2+, as in Problem 4.130, and then titrated with KMnO4 to oxidize the Fe2+ to Fe3+. The balanced equation is 
What is the mass percent Fe in a 2.368 g sample if 48.39 mL of a 0.1116 M KMnO4 solution is needed to titrate the Fe3 + ?

The concentration of an aqueous solution of NaOCl (sodium hypochlorite; the active ingredient in household bleach) can be determined by a redox titration with iodide ion in acidic solution: <img src="https://lightcat-files.s3.amazonaws.com/problem_images/e254d6051f083da1-1669217288584.jpg" alt="" />
Assume that the blue spheres in the buret represent I-ions, the red spheres in the flask represent OCl-ions, the con-centration of the I-ions in the buret is 0.120 M, and the volumes in the buret and the flask are identical. What is the concentration of NaOCl in the flask? What percentage of the I-solution in the buret must be added to the flask to react with all the OCl-ions?
<img src="" alt="" />

(a) How many milliliters of 0.120 M HCl are needed to completely
neutralize 50.0 mL of 0.101 M Ba1OH22 solution?

The concentration of the Sn2+ solution used in Problem 4.130 can be found by letting it react with a known amount of Fe2+. What is the molar concentration of an Sn2+ solution if 23.84 mL is required for complete reaction with 1.4855 g of Fe2O3?

A sample of 8.69 g of Zn1OH22 is added to 155.0 mL of
0.750 M H2SO4. (c) How many moles of ZnSO4
are present after the reaction is complete?

In the lime soda process once used in large scale munici-pal water softening, calcium hydroxide prepared from lime and sodium carbonate are added to precipitate Ca2+ as CaCO3(s) and Mg2+ as Mg(OH)2(s): Ca2+(aq) + CO32-(aq) → CaCO3(s) Mg2+(aq) + 2 OH-(aq) → MgOH2(aq) How many moles of Ca(OH)2 and Na2CO3 should be added to soften (remove the Ca2+ and Mg2+) 1200 L of water in which [Ca2+] = 5.0x10-4 M and [Mg2+] = 7.0x10-4 M?

(d) What is the molarity of the KOH solution prepared in part (c), and how many milliliters of 0.554 M H2SO4 are required to neutralize it?

Citric acid, C6H8O7, is a triprotic acid. It occurs naturally in
citrus fruits like lemons and has applications in food flavouring
and preservatives. A solution containing an unknown
concentration of the acid is titrated with KOH. It requires
23.20 mL of 0.500 M KOH solution to titrate all three acidic
protons in 100.00 mL of the citric acid solution. Calculate the molarity 
of the citric acid solution.

Dichromate ion, Cr2O7 2-, reacts with aqueous iron(II) ion in acidic solution according to the balanced equation 
What is the concentration of Fe2+ if 46.99 mL of 0.2004 M K2Cr2O7 is needed to titrate 50.00 mL of the Fe2+ solution?

Solution Stoichiometry  - Finding Molarity, Mass & Volume

If the following solutions are mixed, is the resulting solution acidic, basic, or neutral?
(a) 65.0 mL of 0.0500 M HClO4 and 40.0 mL of 0.0750 M NaOH

Succinic acid, an intermediate in the metabolism of food molecules, has a molecular weight of 118.1. When 1.926 g of succinic acid was dissolved in water and titrated, 65.20 mL of 0.5000 M NaOH solution was required to neutralize the acid. How many acidic hydrogens are there in a mol-ecule of succinic acid? (LO 4.16)
(a) 1
(b) 2 
(c) 3 
(d) 4

A solution contains Cr3 + ions and Mg2 + ions. The addition of
1.00 L of 1.51 M NaF solution causes the complete precipitation
of these ions as CrF3(s) and MgF2(s). The total mass of the
precipitate is 49.6 g. Find the mass of Cr3 + in the original
solution.

What are the mass and the identity of the precipitate that forms when 30.0 mL of 0.150 M HCl reacts with 25.0 mL of 0.200 M AgNO3?

Find the mass of barium metal (in grams) that must react with
O2 to produce enough barium oxide to prepare 1.0 L of a 0.10 M
solution of OH-.

(b) How many milliliters of 0.125 M H2SO4 are needed to
neutralize 0.200 g of NaOH?

Hard water often contains dissolved Ca2 + and Mg2 + ions. One
way to soften water is to add phosphates. The phosphate ion
forms insoluble precipitates with calcium and magnesium ions,
removing them from solution. A solution is 0.050 M in calcium
chloride and 0.085 M in magnesium nitrate. What mass of sodium
phosphate would you add to 1.5 L of this solution to completely
eliminate the hard water ions? Assume complete
reaction.

Assume that you dissolve 10.0 g of a mixture of NaOH and Ba(OH)2 in 250.0 mL of water and titrate with 1.50 M hydrochloric acid. The titration is complete after 108.9 mL of the acid has been added. What is the mass in grams of each substance in the mixture?

A mixture of acetic acid (CH3CO2H; monoprotic) and oxalic acid (H2C2O4; diprotic) requires 27.15 mL of 0.100 M NaOH to neutralize it. When an identical amount of the mixture is titrated, 15.05 mL of 0.0247 M KMnO4 is needed for complete reaction. What is the mass percent of each acid in the mixture? (Acetic acid does not react with MnO4 equation for the reaction of oxalic acid with MnO4 given in Problem 4.133.)

A 100.0 mL solution containing aqueous HCl and HBr was titrated with 0.1235 M NaOH. The volume of base required to neutralize the acid was 47.14 mL. Aqueous AgNO3 was then added to precipitate the Cl-and Br-ions as AgCl and AgBr. The mass of the silver halides obtained was 0.9974 g. What are the molarities of the HCl and HBr in the original solution?

An acid solution is 0.100 M in HCl and 0.200 M in H2SO4. What
volume of a 0.150 M KOH solution would completely neutralize
all the acid in 500.0 mL of this solution?

Solving Solution Stoichiometry Problems

Find the volume of 0.110 M hydrochloric acid necessary to react
completely with 1.52 g Al(OH)3.

The following three solutions are mixed: 100.0 mL of 0.100 M Na2SO4, 50.0 mL of 0.300 M ZnCl2, and 100.0 mL of 0.200 M Ba(CN)2. 
(b) What is the molarity of each ion remaining in the solution assuming complete precipitation of all insoluble compounds?

Alcohol levels in blood can be determined by a redox reaction with potassium dichromate according to the balanced equation 
What is the blood alcohol level in mass percent if 8.76 mL of 0.049 88 M K2Cr2O7 is required for complete reaction with a 10.002 g sample of blood?

Oxalic acid, H2C2O4, is a toxic substance found in spinach leaves. What is the molarity of a solution made by dissolving 12.0 g of oxalic acid in enough water to give 400.0 mL of solution? How many milliliters of 0.100 M KOH would you need to titrate 25.0 mL of the oxalic acid solution according to the following equation?

(d) If 45.3 mL of a 0.108
M HCl solution is needed to neutralize a solution of KOH,
how many grams of KOH must be present in the solution?

How many milliliters of 0.325 M HCl are needed to react with 16.2 g of magnesium metal?&nbsp;2 HCl (aq) + Mg (s) → MgCl2 + H2 (g)

(b) How many liters of CO2 gas were produced if the density of CO2 is 1.799 g/L?

The reaction of MnO4- with oxalic acid (H2C2O4) in acidic solution, yielding Mn2+ and CO2 gas, is widely used to determine the concentration of permanganate solutions. 
(d) A 1.200 g sample of sodium oxalate (Na2C2O4) is dissolved in dilute H2SO4 and then titrated with a KMnO4 solution. If 32.50 mL of the KMnO4 solution is required to reach the equivalence point, what is the molarity of the KMnO4 solution?
.

What is the molar concentration of a hydrobromic acid solution if it takes 34.12 mL of HBr to completely neutralize 82.56 mL of 0.156 M Ca(OH)­2?&nbsp;2 HBr (aq)&nbsp;+&nbsp;Ca(OH)2 (aq) &nbsp;→ CaBr2 (aq) + 2 H2O (l)

What are the mass and the identity of the precipitate that forms when 55.0 mL of 0.100 M BaCl2 reacts with 40.0 mL of 0.150 M Na2CO3?

A procedure for determining the amount of iron in a sample is to convert the iron to Fe2+ and then titrate it with a solu-tion of Ce(NH4)2(NO3)6: 
What is the mass percent of iron in a sample if 1.2284 g of the sample requires 54.91 mL of 0.1018 M Ce(NH4)2(NO3)6 for complete reaction?

A mixture of FeCl2 and NaCl is dissolved in water, and addi-tion of aqueous silver nitrate then yields 7.0149 g of a pre-cipitate. When an identical amount of the mixture is titrated with MnO4 -, 14.28 mL of 0.198 M KMnO4 is needed for complete reaction. What are the mass percents of the two compounds in the mixture? (Na+ and Cl-do not react with MnO4 -. The equation for the reaction of Fe2+ with MnO4 was given in Problem 4.146.)

Iodine, I2, reacts with aqueous thiosulfate ion in neutral solution according to the balanced equation 
How many grams of I2 are present in a solution if 35.20 mL of 0.150 M Na2S2O3 solution is needed to titrate the I2 solution?

(c) If 18.65 mL
of the caesium hydroxide solution was needed to neutralize a
42.3 mL aliquot of the hydroiodic acid solution, what is the
concentration (molarity) of the acid?

Solution Stoichiometry Example 1

A solution of 105.0 mL of 0.300 M NaOH is mixed with a
solution of 150.0 mL of 0.060 M AlCl3. (e) What is the concentration
of Cl- that remains in solution?

Assume that you have 1.00 g of a mixture of benzoic acid (Mol. wt. = 122) and gallic acid (Mol. wt. = 170)), both of which contain one acidic hydrogen that reacts with NaOH. On titrating the mixture with 0.500 M NaOH, 14.7 mL of base is needed to completely react with both acids. What mass in grams of each acid is present in the original mixture?

(b) When 5.00 g of X is titrated with NaOH, it is found that X has two acidic hydrogens that react with NaOH and that 54.9 mL of 1.00 M NaOH is required to completely neu-tralize the sample. What is the molecular formula of X?

What volume of 0.250 M HCl is needed to react completely with 25.00 mL of 0.375 M Na2CO3? (LO 4.15) 
(a) 75.0 mL
(b) 18.8 mL
(c) 37.5 mL
(d) 33.3 mL

(c) If 55.8 mL of a BaCl2 solution
is needed to precipitate all the sulfate ion in a 752-mg sample
of Na2SO4, what is the molarity of the BaCl2 solution?

Use the solution stoichiometric chart when dealing with calculations involving molarity and/or volume.&nbsp;

What is the minimum amount of 6.0 M H2SO4 necessary to produce
25.0 g of H2( g) according to the reaction between aluminum
and sulfuric acid?
2 Al(s) + 3 H2SO4(aq)¡Al2(SO4)3(aq) + 3 H2( g)

The metal content of iron in ores can be determined by a redox procedure in which the sample is first oxidized with Br2 to convert all the iron to Fe3+ and then titrated with Sn2+ to reduce the Fe3+ to Fe2+. The balanced equation is: 
What is the mass percent Fe in a 0.1875 g sample of ore if 13.28 mL of a 0.1015 M Sn2+ solution is needed to titrate the Fe3+?

How many milliliters of 1.00 M KOH must be added to neutralize the following solutions?
(b) A mixture of 0.300 M HCl (45.0 mL) and 0.250 M NaOH (10.0 mL)

Consider the following balanced chemical equation:&nbsp;H2O+&nbsp;2 MnO4– + 3 SO32-&nbsp; → 2 MnO2 + 3 SO42-+ 2 OH–How many grams of MnO2 (MW:86.94 g/mol) will be created when 25.0 mL of 0.120 M MnO4– (MW:118.90 g/mol) reacts with 32.0 mL of 0.140 M SO32- (MW:80.07 g/mol). &nbsp;

The concentration of a solution of potassium permanganate, KMnO4, can be determined by titration with a known amount of oxalic acid, H2C2O4, according to the following equation: 
What is the concentration of a KMnO4 solution if 22.35 mL reacts with 0.5170 g of oxalic acid? (LO 4.22) 
(a) 0.6423 M
(b) 0.1028 M
(c) 0.4161 M 
(d) 0.2569 M

Ammonium chloride, NH4Cl, is a very soluble salt in water. 
(d) How many grams of silver nitrate do you need to add to the solution 
in part (c) to precipitate all of the chloride as silver chloride?

What is the molar concentration of As(III) in a solution if 22.35 mL of 0.100 M KBrO3 is needed for complete reaction with 50.00 mL of the As(III) solution? The balanced equation is:

Consider the reaction:
Li2S(aq) + Co(NO3)2(aq)¡2 LiNO3(aq) + CoS(s)
What volume of 0.150 M Li2S solution is required to completely
react with 125 mL of 0.150 M Co(NO3)2?

An 8.65-g sample of an unknown group 2 metal hydroxide 
is dissolved in 85.0 mL of water. An acid–base indicator is 
added and the resulting solution is titrated with 2.50 M 
HCl(aq) solution. The indicator changes color, signaling that 
the equivalence point has been reached, after 56.9 mL of the 
hydrochloric acid solution has been added. (b) What is the identity 
of the metal cation: Ca2+, Sr2+, or Ba2+?

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[BOOK CHEM] Clutch Version

Solutions

Solutions represent homogeneous mixtures made of 2 or more components that form a uniform composition.&nbsp;

Osmolarity

Osmolarity (ionic molarity) represents the number of moles of ions per liter of solution.&nbsp;

Gas Evolution Equations

A Gas Evolution Equation is a molecular equation that involves the creation of specific gases.&nbsp;

Molecular Equations

Molecular Equations show reacting molecules involved in a chemical reaction.&nbsp;

Complete Ionic Equations

Complete Ionic Equations show aqueous compounds as fully dissociated ions.&nbsp;

Solubility Rules

The Solubility Rules are a convenient set of guidelines to help us determine if a compound will be soluble or insoluble.

Molarity

Ever wonder how a mass amount such as moles can be converted into the volume amount of liters? Well, molarity serves as the bridge between moles and liters.&nbsp;

Electrolytes

Electrolytes are compounds that can conduct electricity once they are dissolved in a solvent.&nbsp;

Solution Stoichiometry deals with stoichiometric calculations in solutions that involve volume and molarity.

Calculate Oxidation Numbers

Calculating Oxidation Numbers is the first pivotal step in understanding redox reactions.&nbsp;

Dilutions

In Dilutions, a solvent (usually water) is added to a concentrated solution.&nbsp;

Redox Reactions

Redox Reactions (oxidation-reduction reactions) involve transference of an electron(s) between reactants.

Activity Series

Activity Series is a list of single displacement reactions in order of reactivity.

Balancing Redox Reactions: Acidic Solutions

Balancing Redox Reactions requires a new approach that accounts for the transfer of electrons between reactants.

Balancing Redox Reactions: Basic Solutions

Balancing Basic Redox Reactions requires all the same steps as balancing in an acidic solution plus an additional step.